The circulation or movement of solutions through open and closed systems has many technological applications. Mechanical reciprocating pumps, centrifugal pumps, undulating tubes, thermal gradients and propellers have all been used for causing the movement of solutions in appropriate circumstances.
One such common application of a moving solution that exemplifies both the advantages and the problems associated with systems for moving solutions is the circulation of a brine in an indirect heat exchange relationship with a process stream, for example, a gas or liquid undergoing heating or cooling. In this application, the heat exchange solution circulates, usually in a closed system, between the location at which it is in a heat exchange relationship with the process stream and the location at which it is either heated, if it is to heat the process stream, or cooled if it is to cool the process stream. The pumps or other means employed to circulate the solution have a large number of moving parts and suffer breakdowns and otherwise require frequent maintenance and are expensive to operate. Furthermore, the use of pumps and the like to move solutions increases the possibility of contaminating the circulating solution with foreign matter (for example, pump lubricant). Accordingly, a need exists for a system for moving or circulating solutions which is inexpensive to operate, which does not require substantial maintenance and/or which reduces or eliminates the possibility of contamination by foreign matter.
When a solution, U, of solute, X, in solvent, Y, is placed on one side of a semipermeable membrane, M, which is permeable to the solvent, Y, but impermeable to the solute, X, and the pure solvent, Y, is placed on the other side of this semipermeable membrane, M, then an osmotic pressure, P.sub.o, develops in the solution U, such that: EQU P.sub.o =cRT EQ. (1)
Where "c" is the molar concentration of the solute X in the solution U; R is the universal gas constant and T is the absolute temperature. This equation for osmotic pressure was proposed by van't Hoff in 1887 and is sometimes referred to as van't Hoff's Law.
In the above model, when the solution, U, and the pure solvent, Y, exert the same hydrostatic pressure on the membrane, M, the differential external pressure on the membrane P.sub.e, is zero, and the osmotic pressure, P.sub.o, generated in this system produces a net flow rate, J.sub.o, of the solvent, Y, from the side containing the pure solvent through the semipermeable membrane into the side holding the solution, U, of solute, X, in solvent, Y. J.sub.o is, therefore, the net flow rate of liquid through the membrane when the differential external pressure on the membrane, P, is zero.
However, in the same model, if a differential external pressure on the membrane, P.sub.e, is exerted through the solution, U, such that P.sub.e is greater than the osmotic pressure, P.sub.o, then the pure solvent, Y, will flow in the reverse direction, i.e., from the solution, U, side of the semipermeable membrane into the pure solvent side of the semipermeable membrane. Large scale practical application of this is made in reverse osmosis where pure water is obtained from salt water by the use of a semipermeable membrane, pervious to water but impervious to salt.
The movement of molecules and small particles in a quiescent liquid is the direct result of their individual statistical average kinetic energy. For sufficiently large particles this motion is visible under high magnification and is called Brownian motion. For spherical particles the motion is random in direction. For non spherical particles, such as long rods, where the frictional coefficient is smaller for motion parallel to the longitudinal axis than for motion perpendicular to the longitudinal axis, the diffusional coefficient in the direction of the longitudinal axis is greater than the diffusional coefficient in any direction perpendicular to the longitudinal axis.
In the case of a conical shaped Brownian particle the equivalence of all the directions perpendicular to the axis of the cone requires that the diffusional coefficient in all the directions perpendicular to the axis of the cone be identical. The frictional coefficient for a conical shaped Brownian particle along the axis of the cone is less for motion towards the apex than the motion towards the base. Consequently, the diffusional coefficient for a conical Brownian particle along its axis will be greater in the direction of the apex than in the direction of the base.
In addition to the translational motions described above, conical shaped Brownian particles will undergo rotational Brownian motion.
Over all, the total effect is that the conical shaped solute particle meanders through the liquid with a forward bias towards the arbitrary direction in which the apex of the conical shaped solute particle happens to be pointed at that moment.